{
  "id": "2307.03069",
  "version": "v1",
  "published": "2023-07-06T15:35:53.000Z",
  "updated": "2023-07-06T15:35:53.000Z",
  "title": "Deviation Inequalities on the Spectral Norm of Products of Random and Deterministic Matrices",
  "authors": [
    "Guozheng Dai",
    "Zhonggen Su",
    "Hanchao Wang"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:0812.2432, arXiv:0802.3956 by other authors",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the spectral norm of matrices $BA$, where $A$ is a random matrix with independent mean zero subexponential entries, and $B$ is a fixed matrix. We show that the spectral norm of such an $m\\times n$ matrix $BA$ exceeds $\\sqrt{n}+\\sqrt{m}$ with an exponential decay probability. Applying this result, we prove an estimate of the smallest singular value of a random subexponential matrix using an argument in the previous work of Rudelson and Vershynin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-06T15:35:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60F17"
    ],
    "keywords": [
      "spectral norm",
      "deterministic matrices",
      "deviation inequalities",
      "independent mean zero subexponential entries",
      "random subexponential matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}